In an aspect, tomographically reconstructing a 3D image object corresponding to a data set includes for each step in a series of iteration steps, determining an updated object by performing a combined operation, which includes performing an update operation for updating an input object and performing a smoothing operation, and following a last iteration, outputting one of the updated objects as the 3D image object.
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20. A nuclear imaging device for providing a 3D image object, the device comprising:
a detector unit for detecting radiation emitted from within a detecting area and providing a data set indicative of the detected radiation;
an iterative reconstruction unit configured to perform, in each iteration step, including an initial iteration step, to obtain a goodness of fit, a combined operation that includes an update operation for updating an input object, a smoothing operation, and a constraining map determination operation; and
an output port for providing a 3D medical image based on the updated input object.
1. A tomographic reconstruction method for reconstructing a 3D image object corresponding to a data set, the method comprising:
for each step, including an initial step, in a series of iteration steps for tomographic reconstruction to obtain a goodness of fit, determining, with a processor, an update of an input object by performing a combined operation including:
performing an update operation for updating the input object,
performing a smoothing operation on the input object or on the updated input object; and
determining a constraining map associated the smoothing operation; and
following a last iteration occurring due to the goodness of fit, outputting one of the updated input objects as the 3D image object.
19. A non-transitory computer readable medium having included software thereon, the software including instructions to tomographically reconstruct a 3D image object corresponding to a data set, the instructions comprising:
for each step, including an initial step, in a series of iteration steps to obtain a goodness of fit, determining an update of an input object by performing a combined operation including:
performing an update operation for updating the input object;
performing a smoothing operation on the input object or on the updated input object; and
determining a constraining map associated with the smoothing operation; and
following a last iteration, outputting one of the updated objects as the 3D image object.
2. The method of
3. The method of
4. The method of
5. The method of
7. The method of
performing a calculation based on a parameter object, and wherein the smoothing operation is integrated into the update operation to smooth the parameter object.
8. The method of
smoothing a parameter object output from a non-negative least square fit algorithm.
9. The method of
10. The method of
11. The method of
updating the constraining map based on the data set and the updated object of the preceding update operation.
12. The method of
evaluating whether the update of the constraining map is necessary; and
updating the constraining map based on the result of the evaluation, the data set, and an updated object.
13. The method of
updating a parameter of the update operation.
14. The method of
executing a loop over subsets of the data set, wherein the loop includes performing the update operation.
15. The method of
performing the smoothing operation.
16. The method of
updating the constraining map.
17. The method of
evaluating whether an update of the constraining map is necessary; and
updating the constraining map based on the result of the evaluation, the data set and an updated object of the image object.
18. The method of
updating a parameter of the update operation.
21. The nuclear imaging device of
22. The nuclear imaging device of
23. The nuclear imaging device of
24. The nuclear imaging device of
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An embodiment of the invention relates to image reconstruction, and in particular, to image reconstruction using a smoothing operation.
An overview of different reconstruction methods including a pixon method is given in R. C. Puetter et al., “Digital Image Reconstruction: Deblurring and Denoising,” Annu. Rev. Astro. Astrophys., 2005, 43: 139-194; the pixon method is described in R. C. Puetter et al., “The pixon method of image reconstruction,” Astronomical Data Analysis Software and Systems VIII., edited by D. M. Mehringer, R. L,. Plante D. A. Roberts, Astronomical Society of the Pacific, San Francisco, ASP Conference Series 1999, 172, 307-316, the contents of which are herein incorporated by reference. An application of the pixon method to medical planar imaging is discussed in C. A. Wesolowski et al., “Improved lesion detection from spatially adaptive, minimally complex, pixon® reconstruction of planar scintigraphic images”, Comput. Med. Imaging Graph., 2005, 29, 65-81, the contents of which are herein incorporated by reference.
An embodiment of the invention is based in part on the recognition that pixon smoothing can be integrated into iterative image reconstruction, for example, by pixon smoothing an estimated image object or a parameter object used within the iterative image reconstruction.
In an aspect, tomographically reconstructing a 3D image object corresponding to a data set includes for each step in a series of iteration steps, determining an updated object by performing a combined operation, which includes performing an update operation for updating an input object and performing a smoothing operation, and following a last iteration, outputting one of the updated objects as the 3D image object.
In another aspect, a nuclear imaging device for providing a 3D image object includes a detector unit for detecting radiation emitted from within a detecting area and providing a data set indicative of the detected radiation, an iterative reconstruction unit configured to perform, in each iteration step, a combined operation that includes an update operation for updating an input object and a smoothing operation, and an output port for providing the 3D medical image.
Implementations may include one or more of the following features. The smoothing operation may be based on smoothing selected from the group consisting of smoothing based on pixon smoothing, smoothing based on Fourier filtering, smoothing based on wavelet filtering, smoothing based on filtering with a Wiener filter, and smoothing based on filtering with a fixed filter.
Performing the smoothing operation of the combined operation may create a smoothed object, which then is updated by the update operation. Performing the update operation of the combined operation may create an unsmoothed updated object, which then is smoothed by the smoothing operation.
The combined operation may further include performing a first projection operation from a data space to an object space, thereby creating a projected object, and wherein the smoothing operation smoothes the projected object.
The smoothing operation may create a smoothed object and the combined operation may further include, following performance of the smoothing operation, performing a projection operation of the smoothed object from the object space to the data space.
The update operation may include performing the smoothing operation.
Performing the update operation may include performing a calculation based on a parameter object, and the smoothing operation is integrated into the update operation to smooth the parameter object.
The update operation may include smoothing a parameter object of a non-negative least square fit algorithm.
Reconstructing a 3D image object may further include determining a constraining map associated to smoothing selected from the group consisting of smoothing based on pixon smoothing, smoothing based on Fourier filtering, smoothing based on wavelet filtering, smoothing based on filtering with a Wiener filter, and smoothing based on filtering with a fixed filter.
Reconstructing a 3D image object may further include determining a constraining map based on the data set and an initial object.
Each iteration step may further include updating the constraining map based on the data set and the updated object of the preceding update operation. Each iteration step may include the steps of evaluating whether the update of the constraining map is necessary; and updating the constraining map based on the result of the evaluation, the data set, and an updated object. Each iteration step may further include updating a parameter of the update operation.
Each iteration step may further include executing a loop over subsets of the data set, wherein the loop includes performing the update operation. Executing the loop may further include performing the smoothing operation and/or updating the constraining map and/or updating a parameter of the update operation. Executing the loop may further include evaluating whether an update of the constraining map is necessary and updating the constraining map based on the result of the evaluation, the data set and an updated object of the image object.
The update operation may be an update operation of a reconstruction algorithm selected from the group consisting of algorithms based on an ordered subset expectation maximization, algorithms based on a non-negative least square fit, and algorithms based on an ordered subset non-negative least square fit.
The reconstruction unit of the nuclear imaging device may be configured to update the constraining map used within the constraining operation based on an updated image object.
The detector unit of the nuclear imaging device may include a detector system of a positron emission tomography detector system, a single photon computed tomography detector system and/or a computed tomography detector system.
These general and specific aspects may be implemented using a system, a method, a computer readable medium, or a computer program, or any combination of systems, methods, a computer readable medium, or a computer programs.
Certain implementations may have one or more of the following advantages. The constrained tomographic image has a high quality. Combining smoothing, especially pixon smoothing, with the update operation of the tomographic reconstruction can be used to further smooth an object based on the statistics of the data set.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.
Like reference symbols in the various drawings indicate like elements.
The pixon smoothing method described herein is one example of a smoothing operation that constrains the reconstruction. However, operations other than pixon smoothing can also be used. For example, one could smooth by constraining operations that are based on Fourier filtering, application of a Wiener filter, wavelet filtering and/or application of a fixed filter. For such constraining operations, the associated filter functions can be stored in a constraining map corresponding to the pixon map P. An overview of different smoothing methods is given in R. C. Puetter et al., “Digital Image Reconstruction: Deblurring and Denoising,” Annu. Rev. Astro. Astrophys., 2005, 43: 139-194.
The object space is the space in which the result of the image reconstruction is defined and which corresponds to the 3D volume that was imaged using the nuclear imaging system 100. A data space is given by the data points measured with the imaging detector 110.
Within this application “pixon” is used to indicate that a term, method, object etc. refers to the pixon method, and the use of variable volumes when smoothing a 3D image object. For example, the assigned volumes are defined by pixon kernel functions, and the pixon map P stores the information about which of the pixon kernel functions is assigned to which of the object points.
The pixon method provides a smoothed 3D image object I in object space that is a reconstruction of a data set D measured in data space and that fulfills statistical conditions associated with the data set D. The reconstruction in three-dimensions (3D) in the pixon reconstruction unit 120 is based on a combined pixon smoothing and reconstruction algorithm, during which pixon smoothing operations are applied to objects in object space. Each of the pixon smoothing operations, which will be described in more detail in connection with
The pixon smoothing operation is spatially adaptive, as the pixon smoothing operation depends on the values of the measured data set that correspond to that object point. To every object point, one assigns a pixon kernel function, which is the basis for the pixon smoothing operation. Within the pixon reconstruction unit 120, the pixon map P defines which of the pixon kernel functions is assigned to each of the object points.
The pixon method is especially suited for reconstructing an object from a measured data set with a low number of counts and an unavoidable noise contribution. Such data sets are produced, for example, with medical imaging techniques in nuclear medicine, which produce 3D images of, for example, a functional process in a patient's body by using nuclear properties of matter. Examples of such imaging techniques are Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT). For these types of nuclear imaging, one administers a radioactive substance to the patient and detects emitted radiation with a detector system, e.g., with a ring detector for PET or with one or several gamma cameras for SPECT.
Referring to
Pixon Map Determination
The pixon method includes a search for the broadest possible pixon kernel functions that define the largest shape for the smoothing operation at each object point and that together provide an adequate fit of an object, e.g. the 3D image object I, to the data set D. The pixon kernel functions are determined on the basis of a minimum complexity approach and are used for the pixon smoothing operation. An exemplary determination of a pixon map P for the case of low count data having a Poisson-like statistic is described in the co-pending U.S. Published Patent Application No. 2009/0110321, entitled “Determining a pixon map for image reconstruction,” by A. Yahil and H. Vija, filed on even date herewith, the contents of which are herein incorporated by reference. The information about the selected pixon kernel functions is stored in the pixon map P, which assigns a pixon kernel function to each object point.
Combined Smoothing and Reconstruction Algorithm
Iterative image reconstruction methods, such as non-negative least square or Poisson-likelihood algorithms, iteratively fit image models to a measured data set and thus minimize the effect of noise on the image. The result of a reconstruction algorithm is an approximated image that is fit to the measured data set D according to the rules of the algorithm. Within the pixon reconstruction unit 120, such an iterative image reconstruction algorithm is modified by using one or more pixon smoothing operations within the iteration. The smoothing operations act on an object that is created within an iteration step. For example, during an iteration, one can generate an object that is a preliminary approximation of the final image object. In some systems, this object serves as an input object for a next iteration step. However, in the combined pixon smoothing and reconstruction operation 130, the object is first smoothed based on the pixon map P during each iteration, before it is provided as an input object to the next iteration.
The pixon reconstruction unit 120 is configured for image reconstruction that uses an image reconstruction algorithm, in which a pixon smoothing operation is integrated. The image reconstruction algorithm fits a data model, corresponding to the 3D image object, to the measured data set D.
The 3D input object ψ is used to determine an initial pixon map Pi (step 210), which is used for the first pixon smoothing operation within the combined pixon map and reconstruction algorithm. The initial pixon map Pi can be determined with a separate pixon map construction algorithm. In addition, or alternatively the pixon map Pi can be updated (or created) within the combined pixon map and reconstruction algorithm (step 200). An output of the combined pixon map and reconstruction algorithm (step 200) is the final 3D image object I. A final pixon map Pf, which indicates the pixon kernel functions used for the last pixon smoothing operation, can also be provided as an output.
One such condition is a comparison of the stop-criterion, Q(χγ2), with a threshold, τ, which is stored in a tolerance table 340. Thus, in such a goodness-of-fit evaluation of the updated object Iupdate, the quality of the approximated image object can be used to end the iteration. Examples for a quality-controlled iterative reconstruction are given in co-pending U.S. Published Patent Application No. 20090112530, entitled “Controlling the number of iterations in image reconstruction,” by A. Yahil and H. Vija filed on even date herewith, the contents of which are herein incorporated by reference.
Usually, the iteration will start in object space. During the iteration process (indicated by the increase of an iteration counter, iteration (step 400)), an updated object Iupdate is used as an input object for the next iteration step. Thus, each iteration step begins with an improved estimate of the object. As iteration progresses, the updated object Iupdate converges to, for example, a distribution of a radioactive substance administered to the patient.
Within each iteration step, a single OSEM update (step 410) is calculated for a series of subsets of the data set D as indicated by incrementing a subset (step 420). In data space, the single OSEM update (step 410) compares a data model, corresponding to the updated object Iupdate, with the data set D. The OSEM update (step 410) is followed by a test to determine whether all subsets were considered (step 430). After completing an iteration step, i.e., after considering all subsets, a second test determines whether another iteration is necessary (step 440). If no further iterations are necessary, the iteration is stopped and the currently calculated object Iupdate is assigned as the output of the reconstruction, i.e. as the 3D image object I.
Each iteration includes, in addition, to the standard features of an OSEM algorithm, a forward pixon smoothing operation (step 450) and a backward pixon smoothing operation (step 460). The forward pixon smoothing operation (step 450), which is described in more detail in connection with
Pixon Smoothing
Pixon smoothing can be viewed as averaging values of an object over a specific volume (in 3D) defined by the pixon kernel function. The smoothing operation can be written as a matrix operation using a pixon kernel operator K, such that the (smoothed) image object Iα is given by applying the pixon kernel operator K to a pseudo-image object ψ′:
“Pseudo” indicates that the smoothing operation can be understood as a transformation (using the pixon kernel operator K) from a (pseudo-)object space, i.e. the pre-Pixon smoothing space, to the object space of the 3D image object I. Applying the transpose operator of the pixon kernel operator, KT, then projects from the object space back into the pseudo-object space.
In many cases, the smoothing operation is a convolution operation given by:
Convolutions can be calculated, for example, by a direct summation for small pixon kernel functions and by fast Fourier transforms (FFTs) for large pixon kernel functions. If the pixon kernel function can be factorized, a product of operators can be applied to simplify the calculation.
Pixon kernel functions can be discrete or continuous. They are defined over a volume that surrounds an object point. The volume can be limited (over one or more object points) or extend over the complete object space. Examples for 3D pixon kernel functions include a Gaussian function, an inverted paraboloid, or a function ƒ(x;β)=(1+βx2)−1/β
The shapes of the kernel functions can be symmetric, or they can be adjusted in response to a form prevailing in the image object I. Within the shape of the pixon kernel functions, one can weigh the contribution of an object point. A limiting case of a pixon kernel function is the delta-function, in which the pixon smoothed object and the unsmoothed object are identical.
Forward Pixon Smoothing
During the forward pixon smoothing operation (step 450), one repetitively smoothes each object point of the pseudo-object ψ′ over pixon kernel functions, which are specifically assigned to each object point by the pixon map P. In accordance with the above discussed use of the pixon kernel operator K, an input object that is provided to a forward pixon smoothing operation is called a “pseudo-object” ψ′.
The pseudo-object ψ′, the initial image object I0, the kernel pointer kdx, and the pixon map P are also then provided to a single-kernel function forward update (step 520). Output parameters of the single-kernel function forward update (step 520) are the unchanged kernel pointer kdx and an updated image object Ikdx. At the end of each iteration, one determines whether another pixon kernel function update is necessary (step 530). If another update is necessary the kernel pointer kdx is increased (step 540). Otherwise, if all kernel functions have been considered, one assigns the updated image object Ikdx to be the pixon smoothed object Ip. The pixon smoothed object Ip can be used, for example, as an input object of the loop over the subsets.
Then, one determines how much a data point is affected by the current kernel function (step 610). The corresponding calculation uses the pixon map P and the current value of the kernel pointer kdx to determine a temporary field, temp, which is zero if the object point is not affected. The temporary field, temp, has values between 0 and 1 when two kernel functions are used for the smoothing of the object point, and a value of 1 when only the current pixon kernel function is used for smoothing of the object point. For updating each affected object point of the image object Ikdx-1, one adds, to the current value of the image object Ikdx-1, the product of the values of the temporary field, temp, and of the smoothed pseudo-object ψ′kdx of that object point (step 620). The result is the updated image object Ikdx.
Backward Pixon Smoothing
Additionally, or as an alternative to the pixon forward smoothing with the operator K, a backward pixon smoothing can be used within the combined pixon smoothing and reconstruction algorithm. In this case, one generates a smoothed object with a transposed pixon operator KT.
For the smoothing operation, one prepares the initial pseudo-object ψ0 and the kernel pointer kdx, which indicates which one of the pixon kernel functions is applied during the single-kernel backward update. An input object I′ (e.g., the output of the loop over the subsets) and the pixon map P are also used within the update to determine an updated pseudo-object ψkdx. One then evaluates whether to include a further pixon kernel function in the smoothing or whether all kernel functions have been considered, in which case the pseudo-object ψkdx becomes the smoothed pseudo-object ψp. In the case of
Pixon OSEM Algorithm
Alternatively, or in addition, smoothing operations can be applied within the loop over the subsets. For example,
When pixon smoothing is applied within the single OSEM update (step 410), the details of which are shown in
The forward projection projects a pseudo (input) object ψ from object space into data space (step 1200). Object space and data space are related to each other through the nuclear i aging system 100 by the system matrix H. A “forward projection” is an application of the system matrix H to an object in object space. The result of a forward projection is a “projected object” in data space. For example, projecting an estimated image into data space results in a data model Mi of that estimated image:
However, the system matrix H is rarely applied as a matrix multiplication. Instead, it is represented as a product of operators Hn:
H=Hn . . .
H2
H1
Corresponding to the forward projection, the backward projection from the data space into object space can be described as an application of the transpose HT of the system matrix H:
The transpose HT is also rarely applied as a matrix multiplication. Instead, it too is represented as a product of operators:
HT=H1TH2T
. . .
HnT
The pseudo object ψ can be either an initial object or a preceding updated object Iupdate. In the case of an OSEM algorithm, a specific restriction of non-negativity applies to the initial input object.
Referring to
The updated object Iupdate is now used as an input object for the next iteration step. Thus, each iteration step begins with a new estimate of the object. After several iteration steps, the estimates converge during reconstruction to, for example, the distribution of the radioactive substance administered to the patient.
Pixon Map Update
Smoothing operations can be based on constraining maps that provide information about the smoothing itself. An example of a constraining map associated to object points is the pixon map P used for pixon smoothing. The pixon map P is based on the data set D and an object being an estimation of the final 3D image object. When one determines the pixon map P, one statistically evaluates the effect of smoothing the object with a specific pixon kernel function. Thus, the pixon map P depends on the underlying object.
During the reconstruction process of the combined smoothing and reconstruction algorithm (step 200), one iteratively improves the estimation of the final image object I. Thus, one can adapt the pixon smoothing to the latest estimated object by determining an updated pixon map P, the construction of which is then based on the latest estimated object.
One can update the constraining map throughout the combined smoothing and reconstruction algorithm. As an example based on the algorithm shown in
To avoid excessive computational effort arising from the construction of the pixon map, one may wish to control when an update takes place and when it does not. As an exemplary control parameter, one can evaluate a change between the object that was used for the pixon map construction, and the most recent updated object Iupdate. Only if this change is significant will one construct a new pixon map based on the updated object Iupdate. A method to evaluate the change of the object can be based on the quality of the object as given, for example, by the stop-criterion discussed in connection with
Details of such a quality controlled pixon update are shown in
Pixon NNLS Algorithms
In the flowchart of
An iterative cycle is indicated by increasing the increment, iteration (step 1610), and a convergence test (step 1620), which can be used due to the convergence of NNLS algorithms. In the convergence test (step 1620), one compares the updated object Iupdate with a preceding updated object Iupdate-1 and evaluates whether the change of the updated object Iupdate falls within a predetermined convergence limit. If it does, one smoothes the updated image Iupdate with a last pixon smoothing operation (step 460) and assigns the result to be the final image object I. If the updated object Iupdate does not fulfill the convergence test, one updates the parameter set (step 1630) based on the updated object Iupdate and enters the next iteration.
Within the iterative cycle, one applies one or more pixon smoothing operations. In the case of
Within the NNLS update, forward and backward projections occur, for example, when one calculates a distance parameter and a preliminary gradient parameter, which are defined as objects in object space. Additionally, a preconditioning parameter of the NNLS algorithm can be pixon smoothed after being backprojected from data space into object space. These parameter objects can be smoothed before they are used in the calculation of the updated object. They do not represent estimates of the final image object, but the pixon smoothing operation can be applied to any object in object space. This is similar to the case of the OSEM based algorithms, the OSEM updates of which included a pixon smoothing operation when generating the object correction factor Ro.
Additionally,
During execution of the algorithm, one determines estimated objects that converge to the final image object I. Thus, as for the OSEM algorithms discussed in connection with
As for the OSEM based algorithms, one may wish to update the pixon map only when the updated object Iupdate changed significantly. For example, one may control the pixon map update depending on the calculated stop-criterion, Q(χγ2), as indicated in
Modular Reconstruction
A control unit controls the order in which the iterative algorithm (step 2000) applies the modular update operations (step 2010). The control unit can use a manual input of a user. In addition, or alternatively, an automated system can be used that is based, for example, on the quality of the reconstructed image, or the quality of a constructed pixon map. This is indicated in
In
Another example series can include a first pixon map construction, followed by a first set of pixon smoothing operations, an iterative image reconstruction with a predefined number of iterations, a second pixon map construction (or update of the first pixon map), followed by a combined pixon smoothing and reconstruction update operation. An initial reconstruction can be used to provide an initial pseudo-object to the first pixon smoothing operation.
Mathematical Description
The combined pixon smoothing and reconstruction uses a pixon smoothing operation that is inserted into a reconstruction algorithm, preferably with minimal intrusion. The essence of pixon smoothing is to insert additional, adaptive smoothing into the reconstructed image (object).
In object space, the image can be written as
I=Kψ,
where K is the adaptive smoothing kernel and ψ>0 is a non-negative pseudo object.
The reconstruction is an inversion of the noisy projection into data space:
D=HI+N,
where H is the system matrix and N is the (usually Poisson) noise.
Combining the two equations results in
D=HK
ψ+N=W
ψ+N,
with the effective system matrix W being defined by HK.
With the recognition that the effective system matrix W can be used to reconstruct the pseudo image ψ using the same procedure as that used to reconstruct the image I with the system matrix H, a programmatic intrusion can be minimized when the K and H operations are performed sequentially. Thus, in the forward projection, one performs the operation W=HK, and in the backward projection, one performs the operation WT=KT
HT.
The application of the additional K and KT operations can then be effected in separate subroutines, one for the forward projection and one for the backward projection, each comprising the pixon smoothing operation and a projection transformation between object space and data space. Thus, within a combined pixon smoothing and reconstruction algorithm, pixon smoothing can be applied together with one or more projection transformation just as easily as it can be applied to an object of the algorithm that is defined in object space. The combined pixon smoothing and reconstruction algorithm can thus be considered to be a pixon-constrained image reconstruction algorithm.
A standard reconstruction algorithm and a pixon map determination algorithm may precede the combined pixon smoothing and reconstruction algorithm to provide an initial object and an (initial) pixon map. Thus, in a first stage, an initial solution is found using some reconstruction method, e.g., ordered-set-expectation minimization (OSEM) or nonnegative least squares (NNLS) algorithms, which do not contain any Pixon constraints. For example, the K operation can be set to be an identity operation.
In a second stage, the initial solution found in the first stage is used to determine the adaptive K operation from a pixon map calculation. The pixon map calculation can be based on a standard map determination or on a determination, which is specifically adapted to the statistics of the data set. The pixon map calculation itself involves the (unconditioned) forward and backward projections H and HT.
The final 3D image object I is then determined in a third stage, in which the non-trivial K operation is added as an additional constraint to form a combined pixon smoothing and reconstruction algorithm.
Thus, the pixon method can be integrated into a conventional reconstruction algorithm by adding only three insertion points: (i) a K operation optionally added to a forward projection, (ii) a KToperation optionally added to a backward projection, and (iii) a pixon map determination using the H, HT, K, and KT operations. This procedure is completely general and can be applied to any preexisting reconstruction method. All the specifics of the system matrix and the reconstruction method are already embodied in the H and HT operations and their use in the preexisting reconstruction method.
A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit of the invention. For example, Pixon smoothing can be incorporated into data reconstruction algorithms in different technological fields, such as astronomy, communication technology and medical imaging for 3D (image) reconstruction. Thus, a pixon map construction and the pixon smoothing operation can be based on data sets measured in these technology fields.
The order in which the different pixon kernel functions are used during the smoothing operation can be varied, the step size can be varied, or some pixon kernel functions may be considered only in defined areas of the image.
The table F of pixon kernel functions may comprise, for example, in the order of ten spherical pixon kernel functions. If one does not want to impose symmetry, one may use additionally or alternatively elliptical pixon kernel functions. However, asymmetric pixon kernel functions may increase the computational effort, which one can handle, for example, by using specifically designed hardware.
The pixon map P can be provided, for example, as a field of variables defining the pixon kernel functions or as a field of indices, which indicate kernel functions within the table F of the pixon kernel functions.
Various combinations of the combined smoothing and reconstruction described referring to
The pixon smoothing operation may be the calculation of an average of the values of the object points within the volume defined by the corresponding pixon kernel function. The pixon smoothing within the reconstruction can be applied multiple times until the quality of a corresponding data model fulfills a stop-criterion characterizing the goodness-of-fit of a current data model.
The updated objects, which provided as 3D image object may be the most recently updated object. Alternatively, it may be determined based on quality evaluation criteria. Instead of being supplied to a renderer for visualization, the output object can be supplied to a record keeping system (e.g., PACS system) or a system for automatic quantitative diagnosing.
The source of the radiation may be an object or patient positioned within the detecting area of the nuclear imaging system.
It is to be further understood that, because some of the constituent system components and method steps depicted in the accompanying figures can be implemented in software, the actual connections between the systems components (or the process steps) may differ depending upon the manner in which the disclosed method is programmed. Given the teachings provided herein, one of ordinary skill in the related art will be able to contemplate these and similar implementations or configurations of the disclosed system and method.
For example, the numerical and symbolic steps described herein can be converted into a digital program executed, e.g., on a digital signal processor according to methods well known in the art. The digital program can be stored on a computer readable medium such as a hard disk and can be executable by a computer processor. Alternatively, the appropriate steps can be converted into a digital program that is hardwired into dedicated electronic circuits within the compressor that executes the steps. Methods for generating such dedicated electronic circuits based on a given numerical or symbolic analysis procedure are also well known in the art.
Accordingly, other embodiments are within the scope of the following claims.
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